韧度的变量以及路和圈的长度（英文）  

Variation of toughness and the length of paths and cycles

作　　者：高炜[1] 

机构地区：[1]云南师范大学信息学院,云南昆明650092

出　　处：《苏州科技学院学报（自然科学版）》2016年第1期11-16,共6页Journal of Suzhou University of Science and Technology （Natural Science Edition）

基　　金：国家自然科学基金资助项目(11401519)

摘　　要：一般地,计算机网络用图来表示,其中顶点表示站点,边表示站点之间的通道。韧度和它的变量用来衡量网络的易受攻击性。对于无向简单图G,韧度的变量定义为τ(G) =min﹛|S|/ω(G-S)-1ω(G-S)≥2﹜若G不是完全图;τ(G)=∞若G是完全图。文中给出τ-韧度图中最长路和最长圈的长度的界。Computer networks are usually presented with graphs, where vertices represent sites and edges represent channels between sites. Toughness and its variation are used to measure the vulnerability of networks. For an undirected simple graph G, a variation of toughness is defined as τ（G） =min﹛｜S｜/ω（G-S）-1｜ω（G-S）≥2﹜if G is not complete,and τ（G）=∞ if G is complete. This paper presents the bound of length of longest paths and cycles in τ-tough graphs.

关 键 词：图 韧度 韧度的变量 最长路 最长圈 

分 类 号：O157.5[理学—数学]